A magnetic field is invisible, but you can make it 'glow' using tiny defects in diamond — nitrogen-vacancy centers. Each such defect acts as a miniature compass, telling you which way the field points. The problem is that there are many of these compasses, and reading them all in sequence is like transcribing every letter in a thick book by hand.
The authors propose not to visit all positions but to take just a handful of random points, like a restorer reconstructing a mosaic from a few surviving tiles. They used a mathematical trick that guesses the smooth curves of the field from sparse measurements. In a computer model, they managed to assemble a picture from 10,000 pixels using only 25 measurements. The accuracy came out above 0.999 on a scale where 1 is a perfect match.
This approach speeds up the work by dozens of times. Instead of slow point-by-point scanning, you can quickly take a few samples and immediately reconstruct the whole picture. This will be useful not only for diamond sensors but also for other magnetometers — for example, those that look for defects in microchips or monitor brain activity.
A nitrogen-vacancy center in diamond is so sensitive that it can detect the magnetic field from a single electron sitting on a neighboring molecule.